An Interdisciplinary Project at Stowe Middle School

[©Frederick David Abraham, project contributors, and sources]

24,000 miles: they will pass, be tired, and have paddled and skied the same amount, if they started from exactly the same place anywhere on earth.

- 0°: United Kingdom, France, Spain, Algeirs, Mali, Bourkina Fasso, Ghana
- 90$#176: Russia, Mongolia, China, India, Bangladesh
- 180°: Russia, Kiribati, Tuvalu, Fiji
- 270° = 90°W: Canada, United States, Mexico, Guatamala, El Salvador

For rounding up, 10/.33 = 30 steps, and so the curve diverges to the edge of the circle in 30 steps, going around 300°, just 30° past 3/4 of the way around the circle. If the spiral were continued out to 360°, the spiral would be 12 units of distance from the center (36 x .3333 = 12).

These constructions and calculations show how a small error can get bigger (diverge), as one goes around the curves or trajectories. (See figure showing divergence when two spirals are superimposed on the same graph.) Note that this concept,

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The whole sequence to 3 decimal places is:*

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r_{1-9}=0.278, 0.556, 0.833, 1.111, 1,389, 1.667, 1.944, 2.222, 2.500*

r_{10-18}=2.778, 3.056, 3.333, 3.611, 3.889, 4.167, 4.444, 4.722, 5.000

r_{19-27}=5.278, 5.556, 5,833, 6.111, 6.389, 6.667, 6.944, 7.222, 7.500

r_{28-36}=7.778, 8.056, 8.333, 8.611, 8.889, 9.167, 9.444, 9.772, 10.000

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## Polar |
## Making |
## Math of |
## Figures |
## Defs Rel |
## Spiral |
## Syn-Dyn |

Created: 12/23/96 Updated: 1/11/97